Some aspects of nonisothermal crystallization of polymers. I. Relationship between crystallization temperature, crystallinity, and cooling conditions

Crystallization modeling of two semi-crystalline polyamides during material extrusion additive manufacturing

In this work, a heat transfer model is developed for thermally-driven material extrusion additive manufacturing of semicrystalline polymers that considers the heat generated during crystallization by coupling crystallization kinetics with heat transfer. The materials used in this work are Technomelt PA 6910, a semicrystalline hot melt adhesive with sub-ambient glass transition temperature (Tg) and slow crystallization, and PA 6/66, a traditional semicrystalline polyamide with a higher Tg and fast crystallization. The coupled model shows that the released heat during crystallization depends on material selection, with Technomelt PA 6910 and PA 6/66's temperatures increased by less than 1 °C and up to 6.3 °C, respectively, due to enthalpy of crystallization. Increasing the layer time decreases the layer temperature as well as the initial crystallinity. However, its effect on final crystallinity in Technomelt PA 6910 is negligible due to continued crystallization of the material after printing. Experimental validation shows good agreement for Technomelt PA 6910, but consistently underpredicts PA 6/66 crystallinity. Increasing modeled environmental temperature leads to better agreement with experimental results for PA 6/66, suggesting that higher temperatures may have been experienced. Shear-induced crystallization may also be contributing to crystallinity in this material. The results from this model highlight the importance of and interrelationships between material and processing parameter selection and can aid in achieving quality prints from semicrystalline thermoplastics.

Application of Numerical Modeling and Finite Element Analysis in Fused Filament Fabrication: A Review

Additive manufacturing (AM) is not necessarily a new process but an advanced method for manufacturing complex three-dimensional (3D) parts. Among the several advantages of AM are the affordable cost, capability of building objects with complex structures for small-batch production, and raw material versatility. There are several sub-categories of AM, among which is fused filament fabrication (FFF), also commonly known as fused deposition modeling (FDM). FFF has been one of the most widely used additive manufacturing techniques due to its cost-efficiency, simplicity, and widespread availability. The FFF process is mainly used to create 3D parts made of thermoplastic polymers, and complex physical phenomena such as melt flow, heat transfer, solidification, crystallization, etc. are involved in the FFF process. Different techniques have been developed and employed to analyze these phenomena, including experimental, analytical, numerical, and finite element analysis (FEA). This study specifically aims to provide a comprehensive review of the developed numerical models and simulation tools used to analyze melt flow behavior, heat transfer, crystallization and solidification kinetics, structural analysis, and the material characterization of polymeric components in the FFF process. The strengths and weaknesses of these numerical models are discussed, simplifications and assumptions are highlighted, and an outlook on future work in the numerical modeling and FE simulation of FFF is provided.

Viscoelastic Properties of Polypropylene during Crystallization and Melting: Experimental and Phenomenological Modeling

This paper deals with the viscoelastic behavior during crystallization and melting of semicrystalline polymers, with the aim of later modeling the residual stresses after processing in cases where crystallization occurs in quasi-static conditions (in additive manufacturing for example). Despite an abundant literature on polymer crystallization, the current state of scientific knowledge does not yet allow ab initio modeling. Therefore, an alternative and pragmatic way has been explored to propose a first approximation of the impact of crystallization and melting on the storage and loss moduli during crystallization-melting-crystallization cycles. An experimental approach, combining DSC, optical microscopy and oscillatory shear rheology, was used to define macroscopic parameters related to the microstructure. These parameters have been integrated into a phenomenological model. Isothermal measurements were used to describe the general framework, and crystallization at a constant cooling rate was used to evaluate the feasibility of a general approach. It can be concluded that relying solely on the crystalline fraction is inadequate to model the rheology. Instead, accounting for the microstructure at the spherulitic level could be more useful. Additionally, the results obtained from the experiments help to enhance our understanding of the correlations between crystallization kinetics and its mechanical effects.

Non-Isothermal Crystallization Kinetics of PBSu/Biochar Composites Studied by Isoconversional and Model Fitting Methods

Non-isothermal crystallization of Poly(butylene succinate) (PBSu)/biochar composites was studied at various constant cooling rates using differential scanning calorimetry. The analysis of the kinetics data revealed that the overall crystallization rate and activation energy of the PBSu polymer were significantly influenced by the addition of biochar. Specifically, the PBSu/5% biochar composite with a higher filler content was more effective as a nucleation agent in the polymer matrix, as indicated by the nucleation activity (ψ) value of 0.45. The activation energy of the PBSu/5% biochar composite was found to be higher than that of the other compositions, while the nucleation activity of the PBSu/biochar composites decreased as the biochar content increased. The Avrami equation, which is commonly used to describe the kinetics of crystallization, was found to be limited in accurately predicting the non-isothermal crystallization behavior of PBSu and PBSu/biochar composites. Although the Nakamura/Hoffman-Lauritzen model performed well overall, it may not have accurately predicted the crystallization rate at the end of the process due to the possibility of secondary crystallization. Finally, the combination of the Šesták-Berggren model with the Hoffman-Lauritzen theory was found to accurately predict the crystallization behavior of the PBSu/biochar composites, indicating a complex crystallization mechanism involving both nucleation and growth. The K_g parameter of neat PBSu was found to be 0.7099 K², while the melting temperature and glass transition temperature of neat PBSu were found to be 114.91 °C and 35 °C, respectively, very close to the measured values. The Avrami nucleation dimension n was found to 2.65 for PBSu/5% biochar composite indicating that the crystallization process is complex in the composites.

Jeziorny Method Should Be Avoided in Avrami Analysis of Nonisothermal Crystallization

The Jeziorny method treats nonisothermal crystallization data by replacing the variable temperature (T) values with the corresponding values of time and substituting them into the isothermal Avrami plot, ln[-ln(1 - α)] vs. lnt. For isothermal data, the slope of this plot is the Avrami exponent, n and the intercept is the rate constant, k_A. This does not hold for nonisothermal data. Theoretical analysis suggests that in the case of nonisothermal data the intercept cannot be interpreted as k_A, and its "correction" by dividing over the temperature change rate β is devoid of any meaning. In turn, the slope cannot be interpreted as n. It is demonstrated that the slope changes with time and its value depends not only on n but also on the temperature, temperature range, and activation energy of crystallization. Generally, the value of the slope is likely to markedly exceed the n value. The theoretical results are confirmed by analysis of simulated data. Overall, the Jeziorny method as well as other techniques that substitute nonisothermal data into the isothermal Avrami plot should be avoided as invalid and useless for any reasonable Avrami analysis. It is noted that n can be estimated from the nonlinear plot of ln[-ln(1 - α)] vs. T.

Consolidation of Additive Manufactured Continuous Carbon Fiber Reinforced Polyamide 12 Composites and the Development of Process-Related Numerical Simulation Methods

Additive manufacturing of high-performance polymers-such as PA12, PPS, PEEK, and PEKK-combined with industrial-grade carbon fibers with a high fiber volume ratio of up to 60% allows a weight reduction of over 40% compared to classic metal construction. Typically, these 3D-printed composites have a porosity of 10-30% depending on the material and the printing process parameters, which significantly reduces the quality of the part. Therefore, the additive manufacturing of load-bearing structural applications requires a proper consolidation after the printing process-the so-called 'additive fusion technology'-allowing close to zero void content in the consolidated part. By means of the upfront digital modeling of the consolidation process, a highly optimized composite component can be produced while decreasing the number of expensive prototyping iterations. In this study, advanced numerical methods are presented to describe the consolidation process of additive manufactured continuous carbon fiber reinforced composite parts based on the polyamide 12 (PA12) matrix. The simulation of the additive fusion step/consolidation provides immediate accuracy in determining the final degree of crystallization, process-induced deformation and residual stresses, final engineering constants, as well as porosity. The developed simulation workflow is demonstrated and validated with experimental data from consolidation tests on the final porosity, thickness, and fiber-volume ratio.

Influence of Raster Pattern on Residual Stress and Part Distortion in FDM of Semi-Crystalline Polymers: A Simulation Study

In fused deposition modelling (FDM) based on the selected raster pattern, the developed internal thermal residual stresses can vary considerably affecting the mechanical properties and leading to distinct part distortions. This phenomenon is more pronounced in semi-crystalline than amorphous polymers due to crystallisation. Hence, this study focuses on the simulation of the FDM process of a semi-crystalline polymer (polypropylene) with raster patterns such as line (90°/90°), line (0°/90°), zigzag (45°/45°), zigzag (45°/-45°), and concentric from Cura (slicing software). The simulation provides visualisation and prediction of the internally developed thermal residual stresses and resulting warpage with printing time and temperature. The sample with a line (90°/90°) raster pattern is considered as the reference sample in order to compare the relative levels of residual stress and warpage in the other printed/simulated samples. Among the considered raster patterns, the concentric pattern displays the lowest amount of warpage (5.5% decrease) along with a significant drop in residual stress of 21%. While the sample with a zigzag (45°/-45°) pattern showed the highest increase of 37% in warpage along with a decrease of 9.8% in residual stresses. The sample with a zigzag (45°/45°) pattern, exhibited a considerable increase of 16.2% in warpage with a significant increase of 31% in residual stresses. Finally, the sample with a line (0°/90°) raster pattern displayed an increase of 24% increase in warpage with an increase of 6.6% in residual stresses.

Low Temperature Powder Bed Fusion of Polymers by Means of Fractal Quasi-Simultaneous Exposure Strategies

Powder Bed Fusion of Polymers (PBF-LB/P) is a layer-wise additive manufacturing process that predominantly relies on the quasi-isothermal processing of semi-crystalline polymers, inherently limiting the spectrum of polymers suitable for quasi-isothermal PBF. Within the present paper, a novel approach for extending the isothermal processing window towards significantly lower temperatures by applying the quasi-simultaneous laser-based exposure of fractal scan paths is proposed. The proposed approach is based on the temporal and spatial discretization of the melting and subsequent crystallization of semi-crystalline thermoplastics, hence allowing for the mesoscale compensation of crystallization shrinkage of distinct segments. Using thermographic monitoring, a homogenous temperature increase of discrete exposed sub-segments, limited thermal interference of distinct segments, and the resulting avoidance of curling and warping can be observed. Manufactured parts exhibit a dense and lamellar part morphology with a nano-scale semi-crystalline structure. The presented approach represents a novel methodology that allows for significantly reducing energy consumption, process preparation times and temperature-induced material aging in PBF-LB/P while representing the foundation for the processing of novel, thermo-sensitive material systems in PBF-LB/P.

Thermomechanical Behaviour and Interface of Overmoulded Soft Thermoplastic Vulcanizate Elastomers

The influence of melt injection temperature on the thermomechanical behaviour of soft–soft overmoulded vulcanized thermoplastic elastomers (TPV) with different elastic properties was studied. Samples with two different overmoulding temperatures were tested under uniaxial loading conditions. The full deformation and temperature fields in each TPV were determined using digital image correlation technique and infrared thermography, respectively. The maximum interface strength was found to be equal to 70N for a maximum injection temperature of 260∘C, which is consistent with the fact that high temperatures promote interdiffusion between the molten TPV and the TPV insert. The two TPV have different stiffness, leading to a significant change of the interface position along the specimens during stretching and to a significant necking in the softer material. The zone of influence of the interface in terms of stretch gradient is very different in size from one TPV to the other. In addition, thermal investigations have shown that the elasticity of the two TPV is due to both entropic and non-entropic effects, the former being the most significant at large strains.

Crystallization of Polymers under the Influence of an External Force Field

We simulated the crystallization and melting behavior of entangled polymer melts using molecular dynamics where each chain is subject to a force dipole acting on its ends. This mimics the deformation of chains in a flow field but represents a well-defined equilibrium system in the melt state. Under weak extension within the linear response of the chains, the mechanical work done on the system is about two orders of magnitude smaller as compared with the heat of fusion. As a consequence, thermodynamic and simple arguments following the secondary nucleation model predict only small changes of the crystalline phase. By contrast, an increase of the stem length up to a factor of two is observed in our simulations. On the other hand, the lamellar thickening induced by the external force is proportional to the increase of the entanglement length in the melt prior to crystallization as measured by the primitive path method. While the mechanical work done on the system is only a small perturbation for thermodynamics of polymer crystallization, the change of the primitive path is large. This suggests that a strong increase in the lamellar thickness induced, by external deformation, a topological rather than a thermodynamic origin.

Crystallization kinetics and glass-forming ability of rapidly crystallizing drugs studied by Fast Scanning Calorimetry

The use of the amorphous forms of drugs is a modern approach for the enhancement of bioavailability. At the same time, the high cooling rate needed to obtain the metastable amorphous state often prevents its investigation using conventional laboratory methods such as differential scanning calorimetry, X-ray powder diffractometry. One of the ways to overcome this problem may be the application of Fast Scanning Calorimetry. This method allows direct determination of the critical cooling rate of the melt and kinetic parameters of the crystallization for bad glass formers. In the present work, the amorphous states of dopamine hydrochloride and atenolol were created using Fast Scanning Calorimetry for the first time. Critical cooling rates and glass transition temperatures of these drugs were determined. Based on the values of the kinetic fragility parameter, dopamine hydrochloride glass can be considered strong, while atenolol glass is moderately strong. Both model-based and model-free approaches were employed to determine the kinetic parameters of cold crystallization of dopamine and atenolol. The results were compared with the data from isothermal crystallization experiments. The Nakamura crystallization model provides the best description of the crystallization process and can be used to predict the long term stability of the amorphous forms of the drugs. The presented approaches may find applications in predicting the storage time and choosing the optimal storage conditions of the amorphous drugs prone to crystallization.

Consolidation Modeling during Thermoforming of Thermoplastic Composite Prepregs

This article describes the modeling of the compaction/consolidation behavior of thermoplastic composite prepregs during the thermoforming process. The proposed model is principally based on a generalized Maxwell approach. Within a hyperelastic framework, viscoelasticity is introduced for the compaction mode in addition to the in-plane shearing mode by taking into account the influence of the resin and its flow during consolidation. To reveal the evolution of the consolidation level, which reflects the number of voids in the composite, an intimate contact model was used during the process. The model was characterized by a compaction test at a high temperature. It was implemented into a recently developed prismatic solid-shell finite element. The analysis of the thermoforming of a double dome demonstrated the relevance of the consolidation computation in determining the process parameters leading to a composite part free of voids.

Recent Developments in Dispersive Kinetics

In general, chemical reactions proceeding on time scales comparable to, or shorter than, those of internal rearrangements in a reaction system renewing the environment of the reactants (mixing), are dispersive. For dispersive kinetics, as for dispersive transport and dispersive relaxation, many time scales coexist. The rate coefficients for dispersive processes depend on time. For a time-dependent specific reaction rate, using the concept of energy profile along the reaction path, one finds the potential energy barrier separating reactants from products to evolve in time during the course of reaction. The evolution of the energy barrier during the course of reaction is described in terms of energy distribution functions related directly to the distribution function of logarithms of lifetimes calculable from kinetic equations with a time-dependent specific reaction rate. This phenomenological approach is compared with that in which the kinetic equations with time-dependent specific reaction rates are interpreted in terms of the superposition of classical reaction patterns. Special attention is paid to renor-malization of rate coefficients following from the stochastic theory of renewals (structural relaxation) in the reaction system. This phenomenological approach to kinetics is taken as a convenient basis to present a number of comprehensive models of dispersive kinetics developed in the 1990s and to discuss some recently published experimental data to show what one derives directly from experimental data and what the detailed mechanistic models have to account for to be acceptable.

Using optical resonances to control heat generation and propagation in silicon nanostructures

Integrated electronics, photonics and optoelectronics need full control of lattice reconstruction processes in silicon nanostructures at the nanoscale level.

Crystallization Kinetics of Polyamide 12 during Selective Laser Sintering

Selective laser sintering (SLS) of thermoplastic materials is an additive manufacturing process that overcomes the boundary between prototype construction and functional components. This technique also meets the requirements of traditional and established production processes. Crystallization behavior is one of the most critical properties during the cooling process and needs to be fully understood. Due to the huge influence of crystallization on the mechanical and thermal properties, it is important to investigate this process more closely. A commercial SLS polyamide (PA12) powder was measured with differential scanning calorimetry (DSC) to model a wider temperature range. To model isothermal crystallization between 160 and 168 °C, the Avrami model was used to determine the degree of crystallization. For non-isothermal crystallization between 0.2 and 20 K/min, different models were compared including the Ozawa, Jeziory, and Nakamura equations.

Crystallization of Polymers in Processing Conditions: An Overview

In polymer processing, crystallization generally occurs in complex, inhomogeneous and coupled mechanical (flow, pressure), thermal (cooling rate, temperature gradient) and geometrical (surface of processing tools) conditions. A first route to understand crystallization in processing conditions is to design model experiments to isolate the specific influence of a given parameter. The emphasis will be laid here on the influence of: (i) shear flow through rheo-optical measurements using the commercial RheoScope module, (ii) high cooling rates obtained with the modified hot stage Cristaspeed (up to 2 000 °C min−1) and (iii) high pressures in the original Cristapress cell (up to 200 MPa). Numerical simulation is also a useful tool to understand and predict the coupled phenomena involved in crystallization. Based on Avrami's ideas and equations, a general differential formulation of overall crystallization kinetics has been proposed by Haudin and Chenot (2004). It is able to treat both isothermal and non-isothermal cases, and has been extended to crystallization in a limited volume without and with surface nucleation inducing transcrystallinity.

Controlled Growth of Rubrene Nanowires by Eutectic Melt Crystallization

Organic semiconductors including rubrene, Alq₃, copper phthalocyanine and pentacene are crystallized by the eutectic melt crystallization. Those organic semiconductors form good eutectic systems with the various volatile crystallizable additives such as benzoic acid, salicylic acid, naphthalene and 1,3,5-trichlorobenzene. Due to the formation of the eutectic system, organic semiconductors having originally high melting point (T_m > 300 °C) are melted and crystallized at low temperature (T_e = 40.8–133 °C). The volatile crystallizable additives are easily removed by sublimation. For a model system using rubrene, single crystalline rubrene nanowires are prepared by the eutectic melt crystallization and the eutectic-melt-assisted nanoimpinting (EMAN) technique. It is demonstrated that crystal structure and the growth direction of rubrene can be controlled by using different volatile crystallizable additives. The field effect mobility of rubrene nanowires prepared using several different crystallizable additives are measured and compared.

Numerical and Physical Modeling of Polymer Crystallization

In this first paper, we have revisited Avrami's model and cast its basic equations into a differential system. This system is integrated numerically, which avoids unnecessary simplifying assumptions generally used in order to get analytical expressions. This allows us to introduce the variations of nucleation and growth parameters as a function of processing ones (temperature, cooling rate, shear rate, etc.). Our analysis shows that it is necessary to take into account the variation of the initial number of potential nuclei with temperature, which was usually ignored. Finally, an outpout of our calculations is the size distribution of the morphological entities, i. e., a quantitative information on microstructure.

Numerical and Physical Modeling of Polymer Crystallization

Crystallization of thin polypropylene films was performed in isothermal, constant cooling-rate and mixed conditions. The experiments were first analyzed using the classical procedures based on simplified forms (Avrami, Ozawa) of the general Kolmogoroff-Avrami-Evans (KAE) theory. These analyses, which can be applied over an unusually wide transformation range, show that the crystallizations are actually 2 D. Then, a procedure has been established for the determination of the nucleation and growth parameters involved in the theoretical model presented in the first paper of this series. These parameters have been introduced into the model in order to predict the crystallization behavior in isothermal, constant-cooling-rate and mixed-conditions: transformed fraction, number of activated nuclei, final size distribution of semi-crystalline entities. A very good agreement is generally found between predictions and experimental results.

Structure Development in Injection Molding: A 3D Simulation with a Differential Formulation of the Kinetic Equations

The purpose of the present work is to introduce a crystallization law into Rem3D, a 3D code written in C++ and dedicated to the injection molding of polymers. We kept the basic hypotheses of Avrami's model and cast the kinetic equations into a differential system that is solved numerically. The variation of the density of potential nuclei with temperature is taken into account. Furthermore, the distribution of mean spherulite sizes can be deduced from the calculations. The second part of the paper is an experimental study of crystallization in well-controlled conditions (2D, isothermal or constant cooling-rate). It establishes a procedure for the determination of the nucleation and growth parameters used in the theoretical model, and gives a first validation of this model. Finally, the crystallization equations are introduced into Rem3D, in order to assess the feasibility of our new approach. Some typical results concerning the evolution of the transformed volume fraction in injection-molded parts are presented.

Non-Isothermal Simulation of the Film Blowing Process Using Multi-Mode Extended Pom-Pom Model

Plastic films are largely produced using the film blowing process. Branched polymers such as LDPE are commonly used in this process to produce a variety of plastic films. In this study, recently developed eXtended Pom-Pom (XPP) model, which focuses on describing rheological behavior of branched polymers, is employed to analyze the non-isothermal flow in the film blowing process. Furthermore, the Nakamura equation for crystallization kinetics is employed to consider crystallization effects and improve prediction of the state of the stress in the film. Results of the numerical analysis show good agreement with the experimental values reported by Tas (1994) for the bubble shape and film velocity of the LDPE films. Predictions for the strain rates in machine and hoop directions which are critical for the estimation of the stress are also compared with the reported data and showed reasonably good agreement.